Question

Question #af849

Answer 1

`arctan(7/3)-pi\approx -1.976\mbox{ radians}\approx -113.2^{\circ}`

Explanation:

First, mark the point `-(3+7i)=-3-7i` in the complex plane. Note that it is in the 3rd quadrant. This means that its argument, or angle (typically taken to be between `-pi` and `pi`) is `arctan((-7)/(-3))-pi=arctan(7/3)-pi\approx -1.976\mbox{ radians}\approx -113.2^{\circ}`.

You need to subtract `pi` from `arctan(y/x)` in this case because of the fact that the point is in the 3rd quadrant. The arctangent function gives an output between `-pi/2` and `pi/2` radians.

Answer 2

The answer already given is perfectly alright.

Explanation:

Just to make it more clear, it can be stated that argument is measured in anticlockwise direction from positive x axis and it is positive till it is less than 180 degrees. In this case the angle that vector -3-7i makes with x axis is in the third quadrant, hence more than 180 degrees. In this case the angle is measured in clockwise direction , hence it is -1.976 radians.